The procedure is tested on 30 randomly chosen Heston parameters' sets. Both the MC benchmark and the SC procedure are based on populations with \(N_{\texttt {paths}}=3\cdot 10^3\)  paths.
The process \(S(T)\)  is sampled using the COS method [1]} combined with SC (COS-SC) to avoid a huge number of CDF numerical inversions [2]}, and so increase efficiency. Then, we apply the grid-based algorithm of ssec: GeneralPricing. We evaluate the ANN at a reduced number of reference quantiles, and we compute the CVs corresponding to each sample of \(S(T)\)  by means of linear interpolation. The CVs identify the map \(\tilde{g}\) , which is employed for the conditional sampling. fig: ConditionalDistributiona shows the cloud of points (for parameters' Set III in tab: ResultCondAsian) of the bivariate distribution \((S(T), A(S))\)  generated using the procedure against the MC benchmark, while fig: ConditionalDistributionb only focuses on the marginal distribution of \(A(S)\) . We can appreciate a good matching between the two distributions.
